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A Note on the Fibonacci Quotient Fp-ε/p

Published online by Cambridge University Press:  20 November 2018

H. C. Williams*
Affiliation:
Department of Computer Science, University of Manitoba Winnipeg, Manitoba, R3T 2N2 Canada
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Abstract

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In this note a formula analogous to Eisenstein's well known formula is presented for Fp-ε/p, where Fn is the nth Fibonacci number (F0 = 0, F1 = 1), p an odd prime, and

This formula is:

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Andrews, G. H., Some Formulae for the Fibonacci sequence with generalizations, Fib. Quart., 7 (1969), 113-130.Google Scholar
2. Brillhart, J., Tonascia, J., and Weinberger, P., On the Fermat quotient, Computers in Number Theory, Academic Press, London and New York, 1971, pp 213-222.Google Scholar
3. Dickson, L. E., History of the Theory of Numbers, Vol. 1, Chelsea, New York, 1952.Google Scholar
4. Lehmer, D. H., An extended theory of Lucas' functions, Annals of Math. (2) 31 (1930), 419-448.Google Scholar
5. Wall, D. D., Fibonacci series modulo m, Amer. Math. Monthly. 67 (1960), 525-532.Google Scholar